Josephson effects in dilute Bose-Einstein condensates

We propose an experiment that would demonstrate the de and ac Josephson effects in two weakly linked Bose-Einstein condensates. We consider a time-dependent barrier, moving adiabatically across the trapping potential. The phase dynamics are governed by a "driven-pendulum" equation, as in current-driven superconducting Josephson junctions. At a critical velocity of the barrier (proportional to the critical tunneling current), there is a sharp transition between the de and ac regimes. The signature is a sudden jump of a large fraction of the relative condensate population. Analytical results are compared with a numerical integration of the Gross-Pitaevskii equation, inn experimentally realistic situation.